AP EAMCET · Maths · Quadratic Equation
Let \(\alpha\) and \(\beta\) be the roots of the equation \(p x^2+q x+r=0, p \neq 0\). If \(p, q, r\) are in AP and \(\frac{1}{\alpha}+\frac{1}{\beta}=4\), then the value of \(|\alpha-\beta|\) is
- A \(\frac{\sqrt{61}}{9}\)
- B \(\frac{2 \sqrt{17}}{9}\)
- C \(\frac{\sqrt{34}}{9}\)
- D \(\frac{2 \sqrt{13}}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \sqrt{13}}{9}\)
Step-by-step Solution
Detailed explanation
Since, \(\alpha\) and \(\beta\) are roots of quadratic equation \(p x^2+q x+r=0, p \neq 0\) and \(p, q, r\) are in AP such that \(\frac{1}{\alpha}+\frac{1}{\beta}=4\) ...(i) Let the \(p=q-d\) and \(r=q+d\), where \(d\) is the common difference of AP \(\therefore\) Sum of the…
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